When solving equations involving squares of variables, taking square roots on both sides produces both positive and negative solutions, meaning quadratic equations typically have two solutions. For example, in (x - 9)² = 81, taking the square root gives x - 9 = 9 or x - 9 = -9, resulting in x = 18 or x = 0.
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(x - 9)^2 = 81. Literally 90% got it wrong!Hinzugefügt:
Welcome everyone. So, yes, literally everyone thought that the answer for this one was supposed to be just six.
6 minus 2 Sorry.
Sorry, my bad. A lot of everyone thought that the answer for this one was supposed to be what? Four. 4 minus 2 the whole square should get you 2 squared which gets you four. This is correct.
One of the answers is correct, but since the degree of the entire equation is two, there's a very high chance that we will have another value of x as well.
Now, whenever there is an square involving a variable, okay, and you want to take square roots on both sides, the value of that square root comes in positive and negative values, okay? Because there is a variable involved.
So, now I can say my x minus 2 is equal to either 2 or I can say x minus 2 is equal to minus 2.
When you add two on both sides, you get the value of x over here as four. And here, you get the value of x as nothing but zero.
Okay? So, now like we saw that four is absolutely correct, but let's see for zero. 0 minus 2 the whole square. That gets you minus 2 the whole square. Now, square of a negative number still gets you a positive value. So, here we can say the value of x is either four or zero. I hope this is very, very clear to everyone. That's it for today. I will see you in the next video.
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